Preheat oven to 350° (F). Line a 9 inch round baking pan with parchment paper and grease well.
In a large bowl whisk together the flour, baking powder, baking soda, and salt; set aside.
In a separate bowl, whisk together the oil, milk, butter, vanilla, and 1/4 cup of the clementine juice; set aside.
Mix the granulated sugar and zest together until fragrant and the sugar has taken on an slightly orange hue. Combine the sugar and eggs in a large bowl or stand mixer fitted with the paddle attachment and beat on medium-high until light and fluffy, 2 to 3 minutes.
Reduce speed to low and add the flour mixture and the milk mixture alternately, beginning and ending with the flour mixture, mixing well between additions.
Transfer the batter to the prepared pan and bake until a toothpick inserted in the center comes out clean, about 45-50 minutes. Cool the cake in the pan for at least 20 minutes, then transfer to a wire rack to cool completely.
Combine the confectioners sugar and the remaining clementine juice in a small bowl; whisk until smooth. Drizzle over the cooled cake. Let set before serving.
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